Elementary fractal geometry. 5. Weak separation is strong separation

arXiv:2404.04892v1 Announce Type: cross
Abstract: For self-similar sets, there are two important separation properties: the open set condition and the weak separation condition introduced by Zerner, which may be replaced by the formally stronger finite type property of Ngai and Wang. We show that any finite type self-similar set can be represented as a graph-directed construction obeying the open set condition. The proof is based on a combinatorial algorithm which performed well in computer experiments.

abstract arxiv cs.cl elementary fractal geometry math.ds property set show type